On one side is a crowd of Republicans trying to look presidential. On the other side is a lone Democrat trying to look normal.

There was Senator Marco Rubio, Republican of Florida, seeking to appear statesmanlike at a rally on Monday evening as he joined the race for the White House in 2016. There was Gov. Scott Walker of Wisconsin, another likely Republican contender, leading a trade mission to Germany, France and Spain this week. Senator Rand Paul of Kentucky is coming off a five-state chartered-jet trip to kick off his campaign, and former Gov. Jeb Bush of Florida was in the swing state of Ohio on Tuesday to outline his economic agenda for business leaders.

Confident that her command of the world stage is well known — hey, Mr. Walker, I visited 112 countries as secretary of state; let me know when you get to Togo — Mrs. Clinton used her announcement video on Sunday to position herself as just one of many Americans (mothers, families, factory workers, gay fiancés) getting ready for big changes. With its progressive themes and checklist of ethnicities, the video looked like an Allstate ad selling anti-Republican insurance.

That day, Mrs. Clinton also set out in a van for Iowa, making unannounced pit stops like an everyday American in hopes of impressing (and hopefully not freaking out) fellow travelers with her suddenly accessible self. It was not your typical American road trip: The Secret Service was driving, two aides sat where Bill and Chelsea might, and presumably no one asked, “Are we there yet?” or demanded to watch a Disney DVD.

Then, in Iowa on Tuesday, Mrs. Clinton held a low-key round table with community college students to talk about their futures and hopes, at one point empathizing with a young woman who said her disabled sister would benefit from year-round schooling. Mrs. Clinton’s suggestion that she would support a constitutional amendment on campaign finance reform seemed almost offhand compared with her attempts to engage with the students.

The emergence of folksy Hillary and the ready-to-lead Republicans clearly signals the start of the Perception Primary, during which candidates seek to erase their deficits and persuade voters to see them differently.

“Mrs. Clinton knows that her image is elite, aloof and disconnected to average voters, while Republicans like Rubio, Walker and Paul each know they are perceived as untested and not ready for prime time,” said Richard Tafel, the founder of Log Cabin Republicans, a gay advocacy group, and an adviser to nonprofit groups about public policy. “The irony is that each party has to pretend to be like the other. The dynastic Clintons are pretending to be average Joes, while the average-Joe Republicans are pretending to be powerful global leaders.”

Steve Elmendorf, a Democratic strategist, said the Republican contenders had to clear the highest hurdle for a presidential candidate: “convincing voters they are up to the job.”

He believes that Mrs. Clinton has already passed that test, given her record and experience, and now needs to concentrate on connecting with people. “Her challenge is to look less presidential and focus voters on her message on middle-class economics,” Mr. Elmendorf said.

But perception can cut different ways: The danger for all of the candidates is that they will ultimately be seen as phony, given that voters have plenty of experience sniffing out the truth about politicians.

Mitt Romney sought to connect with broad cross sections of Americans during his presidential campaigns in 2008 and 2012, but many voters came to see him as a wealthy man with policy ideas aimed at helping people like himself. Al Gore tried to dress in earth tones in hopes of relating to more voters in 2000, while Michael S. Dukakis, a wonk’s wonk, tried to appear tough on defense issues by riding in a tank.

Mrs. Clinton plans to avoid the cities of Iowa in her inaugural campaign trip this week, focusing instead on coffee shops, a community college’s satellite campus and a family-owned business. Big rallies in major media markets would put her at a remove from voters and suggest that she is simply looking for a coronation as the Democratic nominee, her political advisers say.

Some Clinton supporters in Iowa and New Hampshire — the states she is visiting first, which have early nominating contests — believe that her down-home style is an authentic reaction to the need to reach out and fight for support in both states.

“It’s never a walk in the park winning elections in New Hampshire, and I think there will be one or two other Democratic candidates who could become formidable by coming up and campaigning and meeting voters,” said Kathy Sullivan, the Democratic national committeewoman from New Hampshire. “It’s been eight years since the last campaign, so she needs to introduce herself again, and doing a lot of small-scale events and having back-and-forth conversations with voters show that nothing is being taken for granted.”

But some Republicans contend that voters will not accept Mrs. Clinton as one of the “everyday Americans” that she featured in her video and vowed to fight for as president.

“Hillary didn’t become Hillary by being one of the gals; she became Hillary by not being one of the gals, but by being one of the guys, only smarter and craftier,” said Rich Galen, a Republican strategist and onetime aide to Newt Gingrich, the former House speaker. “The danger for Clinton is she has made a career of not being of the people. She has been a cipher, easily changing from leader to victim as circumstances dictate.”

While Mrs. Clinton has the spotlight all to herself for now in the Democratic field, as many as a dozen Republicans are jockeying for attention and looking for ways to be taken seriously.

Mr. Rubio, in his kickoff speech on Monday, sought to sound presidential by touching on issues at home (taxes) and abroad (support for Israel). But he also framed his White House aspirations around himself — with many references to “I,” “me” and “my” — rather than around ordinary Americans, as Mrs. Clinton did in her video. He got deeply personal only in talking about his immigrant parents, though he sidestepped any real discussion about the nation’s immigration system (which once made him a target of conservative ire when he tried to fix it with a comprehensive plan).

Mr. Rubio and most of his Republican rivals will be in New Hampshire this weekend for a state party summit meeting, huddling with groups of elected officials and party activists to make their case. So far, no candidate has risen above the rest.

“My head tells me that Jeb Bush is the only Republican looking presidential at this point, but my heart vacillates a little,” said Barry Wynn, a major Republican donor from South Carolina. “I’ve heard people say, when they listen to Bush in person, he can come across as presidential. But he and the other Republicans need to become sharper, more sure-footed, if one of them is going to beat Hillary and her I’m-like-you message.”